标题： 计算有限半群中不在 ECom 中的行列式的一步 显示英文标题

标题： A step to compute the determinant of finite semigroups not in ECom

摘要： 本文的目的是开始研究有限半群类中非零行列式的计算，这类半群具有非交换幂等元对。 本文专注于一类被称为$\ll$-光滑半群的半群。 该计算适用于半群代数上MacWilliams定理扩展的背景下，用于编码问题。 显示英文摘要

摘要： The purpose of this paper is to begin studying the computation of the nonzero determinant of semigroups within the class of finite semigroups that possesses a pair of non-commutative idempotents. This paper focuses on a class of these semigroups introduced as $\ll$-smooth semigroups. This computation is applicable in the context of the extension of the MacWilliams theorem for codes over semigroup algebras.